Combustion systems and associated methods are disclosed herein. In some embodiments, a combustion system comprises a first combustion zone, a second combustion zone downstream of the first combustion zone, and a heat module thermally coupled to the first combustion zone and/or second combustion zone. The first combustion zone is configured to (i) receive and combust preheated air and a first fuel and (ii) generate a first exhaust gas, and the second combustion zone is configured to (i) receive and combust the first exhaust gas and a second fuel and (ii) generate a second exhaust gas. The first exhaust gas can have a first excess air and the second exhaust gas can have a second excess air less than the first excess air. The heat module can comprise a thermionic converter or another heat-to-electricity converter able to generate a power output.